Has nothing to do with knowing the answer, and everything to do with infinite persistence. I believe any current-generation LLM can, given an environment where it can experiment rapidly, do anything.
LLMs aren't going to make you live forever. This is a marketing scam. They are stateless statistical models that spit out words. Thats it.
Even outside of controls based games, LLMs fail on sokoban like puzzles weirdly enough, see MazeBench, they’re also not that good at chess, probably around 1600 elo.